Currently, methods for encoding an audio signal that compress the amount of data of multichannel audio signals of three or more channels are being developed. As one of such encoding methods, an MPEG Surround method standardized by the Moving Picture Experts Group (MPEG) is known. In the MPEG Surround method, for example, 5.1-channel (5.1ch) audio signals to be encoded are subjected to a time-frequency transform, and frequency signals obtained by the time-frequency transform are downmixed, thereby generating frequency signals of three channels. The frequency signals of the three channels are further downmixed, and, as a result, frequency signals corresponding to stereophonic signals of two channels are calculated. The frequency signals corresponding to the stereophonic signals are then encoded using an Advanced Audio Coding (AAC) encoding method and a Spectral Band Replication (SBR) encoding method. On the other hand, in the MPEG Surround method, when the 5.1ch signals are downmixed to generate the signals of the three channels and when the signals of the three channels are downmixed to generate the signals of the two channels, spatial information indicating the diffusion of a sound or the location of a sound is calculated and encoded. Thus, in the MPEG Surround method, the stereophonic signals generated by downmixing the multichannel audio signals and the spatial information whose amount of data is relatively small are encoded. Therefore, in the MPEG Surround method, the efficiency of compression higher than in a case in which the signal of each channel included in the multichannel audio signals is separately encoded.
In the MPEG Surround method, in order to reduce the amount of information to be encoded, the frequency signals of the three channels are divided into stereophonic frequency signals and two channel prediction coefficients and encoded. The channel prediction coefficients are coefficients for performing predictive coding on a signal of one of the three channels on the basis of the signals of the other two channels. A plurality of channel prediction coefficients are stored in a table called a “code book”. The code book is used to improve the efficiency of bits used. When an encoder and a decoder have a predetermined common code book (or a code book created using a common method), important information may be transmitted with a smaller number of bits. In decoding, a signal of one of the three channels is reproduced on the basis of the channel prediction coefficients. Therefore, in encoding, the channel prediction coefficients are selected from the code book.
As a method for selecting the channel prediction coefficients from the code book, a method has been disclosed in which an error defined by a difference between a channel signal before predictive coding and a channel signal after the predictive coding is calculated using all the channel prediction coefficients stored in the code book, and a channel prediction coefficient with which the error caused by the predictive coding becomes smallest is selected. In Japanese National Publication of International Patent Application No. 2008-517338, a method is disclosed in which a channel prediction coefficient with which an error becomes smallest is calculated using a calculation method adopting a method of least squares.